Lesson 12 | Solving One-Variable Equations | 8th Grade Mathematics

Objective

Solve and graph inequalities with variables on both sides of the inequality (optional).

Common Core Standards

Core Standards

The core standards covered in this lesson

A.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Reasoning with Equations and Inequalities

A.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Foundational Standards

The foundational standards covered in this lesson

7.EE.B.4.B

Expressions and Equations

7.EE.B.4.B — Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Solve inequalities with variables on both sides and use substitution to check answers.
Accurately multiply and divide with negative coefficients in inequalities, paying close attention to the direction of the inequality symbol.
Graph solutions to inequalities.
Write, solve, and interpret solutions to inequalities for applications.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Lessons 11 and 12 extend on 7.EE.4b and bridge a gap to high school standard A.REI.3. Inequalities are not included in the 8th grade standards, but this is a natural extension of students’ work with equations from earlier in the unit, especially now that students are able to work with more complex equations and inequalities. These two lessons can be treated as optional.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Solve the inequality. Then pick a value for $$x$$ and check your answer. Lastly, graph your solution on a number line.

$$7-{2\over3}x>2+x$$

Guiding Questions

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Problem 2

Solve the inequality.

$${\frac{x-7}{3}\leq \frac{2(x-1)}{8}}$$

Guiding Questions

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Problem 3

Lindsay and Kiana work at the same restaurant. Lindsay earns $12.75 per hour and Kiana, who has been working there longer, earns $15.25 per hour. One week, both girls work the same number of hours at the restaurant, but Lindsay spends $37 and Kiana spends $55. At the end of the week, Lindsay has more money left than Kiana. What is the greatest number of hours the girls could have worked for this to be true?

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

Fishtank Plus Content

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Solve the inequality.

$${\frac{-2x+1}{4}< \frac{3x-6}{6}}$$

Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Include problems that cover all types of equations and inequalities.
Include application problems that cover all types of equations and inequalities; students determine if an equation or inequality best represents the situation.

Kuta Software Free Algebra 1 Worksheets Inequalities — Multi-Step Inequalities (Use inequalities with variables on both sides.)
Kuta Software Free Pre-Algebra Worksheets Inequalities — Multi-Step Inequalities (Use inequalities with variables on both sides.)

Lesson 11

Lesson Map

Topic A: Simplifying Expressions and Verifying Solutions

Write equivalent expressions using properties of operations and verify equivalence using substitution.

8.EE.C.7

Define a solution to an equation. Solve and check solutions to 1 and 2 step equations.

8.EE.C.7

Topic B: Analyzing and Solving Equations in One Variable

Justify each step in solving a multi-step equation with variables on one side of the equation.

8.EE.C.7.A 8.EE.C.7.B

Write and solve multi-step equations to represent situations, with variables on one side of the equation.

8.EE.C.7.B

Model with equations using a three-act task.

8.EE.C.7

Solve equations with variables on both sides of the equal sign.

8.EE.C.7

Write and solve multi-step equations to represent situations, including variables on both sides of the equation.

8.EE.C.7

Understand that equations can have no solutions, infinite solutions, or a unique solution; classify equations by their solution.

8.EE.C.7.A

Solve and reason with equations with three types of solutions.

8.EE.C.7.A

Use equations to model a business plan and determine the break-even point.

8.EE.C.7

Topic C: Analyzing and Solving Inequalities in One Variable

Solve and graph inequalities with variables on one side of the inequality (optional).

A.REI.B.3

Solve and graph inequalities with variables on both sides of the inequality (optional).

A.REI.B.3

Solving One-Variable Equations

Objective

Common Core Standards

Core Standards

Reasoning with Equations and Inequalities

Foundational Standards

Expressions and Equations

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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